Here is something on the moon eyed people from History, Myths, and Sacred
Formulas of the Cherokees by James Mooney:
page 22
all below is quoted from his book.

"There is a dim but persistent tradition of a strange white race preceding
the Cherokee, some of the stories even going so far as to locate their
former settlements and to identify them as the authors of the ancient works
found in the country. The earliest reference appears to be that of Barton
in 1797, on the statement of a gentleman whom he quotes as a valuable
authority upon the southern tribes.

"The Cheerake tell us, that when they first arrived in the country which
they inhabit, they found it possessed by certain "moon-eyed people," who
could not see in the day-time. These wretches they expelled."

He seems to consider them an albino race. Haywood, twenty-six years later,
says that the invading Cherokee found "white people" near the head of the
Little Tennessee, with forts extending thence down the Tennessee as far a
Chickamouga creek. He gives the lacation of three forts. The Cherokee made
war against them and drove them to the mouth of Big Chickamauga creek, where
they entered into a treaty and agreed to remove if permitted to depart in
peace. Permission being granted, they abandoned the country. Elsewhere he
speaks of this extirpated white race as having extended into Kentucky and
probably also into western Tennessee, according to the concurrent traditions
of different tribes. He describes their houses, on what authority is not
stated, as having been small circular structures of upright logs, covered
with earth which had been dug out from the inside."
also page 23
"Harry Smith, a halfbreed born abut 1815, father of the late chief of the
East Cherokee, informed the author that when a boy he had been told by an
old woman a tradition of a race of very small people, perfectly white, who
once came and lived for some time on the site of the ancient mound on the
northern side of Hiwassee, at the mouth of Peachtree creek, a few miles
above the present Murphy, North Carolina. They afterward removed to the
West. Colonel Thomas, the white chief of the East Cherokee, born about the
beginning of the century, had also heard a tradition of another race of
people, who lived on Hiwassee, opposite the present Murphy, and warned the
Cherokee that they must not attempt to cross over the south side of the
river or the great leech in the water would swallow them. They finally
went west, "long before the whites came." The two stories are plainly the
same, although told independently and many miles apart."
end quote.